High-order L2 stable multi-domain finite difference method for compressible flows
Abstract
Computational fluid dynamics can be used to gain deeper insight into compressible flow physics, but current limitations in numerical methods, computing hardware, data analysis, and grid adaptation prevent computational analysis from achieving its potential impact. Toward overcoming the first limitation, a new, mathematically rigorous, high-order finite difference method for simulating compressible fluid flows in multi-domain configurations has been developed. This approach facilitates an L2-stability proof for approximate solutions of the Navier-Stokes equations; satisfying nonlinear entropy stability in the domain interior and at multi-block interfaces; and satisfying linear energy stability at domain boundaries. This stability property enables increased robustness and flexibility in simulations of flow configurations that contain shocks and discontinuous geometric features. An analysis is initially developed for general conservation laws based on high-order summation-by-parts finite difference methods and simultaneous approximation term boundary and interface conditions. Stability conditions are derived based on this method of analysis, and numerical methods that satisfy these stability conditions are developed. The resultant numerical approach is applied to simulations of a normal shock propagating past a cylinder, a supersonic flow over a cylinder in a duct, and a transitional Mach 6 boundary layer on an isentropic compression ramp.
Degree
Ph.D.
Advisors
Frankel, Purdue University.
Subject Area
Mechanical engineering
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